Complex problem solving (CPS) emerged in the last 30 years in Europe as a new part of the psychology of thinking and problem solving. This paper introduces into the field and provides a personal view. Also, related concepts like macrocognition or operative intelligence will be explained in this context. Two examples for the assessment of CPS, Tailorshop and MicroDYN, are presented to illustrate the concept by means of their measurement devices. Also, the relation of (...) class='Hi'>complex cognition and emotion in the CPS context is discussed. The question if CPS requires complex cognition is answered with a tentative “yes.”. (shrink)

Complex problem solving (CPS) and related topics such as dynamic decision-making (DDM) and complex dynamic control (CDC) represent multifaceted psychological phenomena. In a broad sense, CPS encompasses learning, decision-making, and acting in complex and dynamic situations. Moreover, solutions to problems that people face in such situations are often generated in teams or groups. In turn, this adds another layer of complexity to the situation itself because of the emerging issues that arise from the social dynamics (...) of group interactions. This framing of CPS means that it is not a single construct that can be measured by using a particular type of CPS task (e.g. minimal complex system tests), which is a view taken by the psychometric community. The proposed approach taken here is that because CPS is multifaceted, multiple approaches need to be taken to fully capture and understand what it is and how the different cognitive processes associated with it complement each other. (shrink)

In this paper, we bring together research on complex problem solving with that on motivational psychology about goal setting. Complex problems require motivational effort because of their inherent difficulties. Goal Setting Theory has shown with simple tasks that high, specific performance goals lead to better performance outcome than do-your-best goals. However, in complex tasks, learning goals have proven more effective than performance goals. Based on the Zurich Resource Model, so-called motto-goals should activate a person’s resources (...) through positive affect. It was found that motto-goals are effective with unpleasant duties. Therefore, we tested the hypothesis that motto-goals outperform learning and performance goals in the case of complex problems. A total of N = 123 subject participated in the experiment. In dependence of their goal condition, subjects developed a personal motto, learning, or performance goal. This goal was adapted for the computer-simulated complex scenario Tailorshop, where subjects worked as managers in a small fictional company. Other than expected, there was no main effect of goal condition for the management performance. An unexpected gender effect revealed better performance for men than women, pointing to a potential stereotype threat. As hypothesized, motto goals led to higher positive and lower negative affect than the other two goal types. Even though positive affect decreased and negative affect increased in all three groups during Tailorshop completion, participants with motto goals reported the lowest rates of negative affect. Exploratory analyses investigated the role of affect in complex problem solving via mediational analyses and the influence of goal type on perceived goal attainment. (shrink)

In the last 20 years, a stream of research emerged under the label of „complex problem solving“ (CPS). This research was intended to describe the way people deal with complex, dynamic, and intransparent situations. Complex computer-simulated scenarios were as stimulus material in psychological experiments. This line of research lead to subtle insights into the way how people deal with complexity and uncertainty. Besides these knowledge-rich, realistic, intransparent, complex, dynamic scenarios with many variables, a second (...) line of research used more simple, knowledge-lean scenarios with a low number of variables („minimal complex systems“, MCS) that have been proposed recently in problem-solving research for the purpose of educational assessment. In both cases, the idea behind the use of microworlds is to increase validity of problem solving tasks by presenting interactive environments that can be explored and controlled by participants while pursuing certain action goals. The main argument presented here is: both types of systems - CPS and MCS – can only be dealt with successfully if causal dependencies between input and output variables are identified and used for system control. System knowledge is necessary for control and intervention. But CPS and MCS differ in their way of how causal dependencies are identified and how the mental model is constructed; therefore, they cannot be compared directly to each other with respect to the cognitive processes that are necessary for solving the tasks. Knowledge-poor MCS tasks address only a small fraction of the cognitive processes and structures needed for knowledge-rich CPS situations. (shrink)

The assumption that positive affect leads to a better performance in simple cognitive tasks has become well established. We address the question whether positive and negative emotions differentially influence performance in complex problem-solving in the same way. Emotions were induced by positive or negative feedback in 74 participants who had to manage a computer-simulated complex problem-solving scenario. Results show that overall scenario performance is not affected, but positive and negative emotions elicit distinguishable problem- (...) class='Hi'>solving strategies: Participants with negative emotions are more focused on the seeking and use of information. We discuss methodological requirements for investigating emotion influences in complex and dynamic cognitive tasks. (shrink)

The assumption that positive affect leads to a better performance in simple cognitive tasks has become well established. We address the question whether positive and negative emotions differentially influence performance in complex problem-solving in the same way. Emotions were induced by positive or negative feedback in 74 participants who had to manage a computer-simulated complex problem-solving scenario. Results show that overall scenario performance is not affected, but positive and negative emotions elicit distinguishable problem- (...) class='Hi'>solving strategies: Participants with negative emotions are more focused on the seeking and use of information. We discuss methodological requirements for investigating emotion influences in complex and dynamic cognitive tasks. (shrink)

Following Marr’s famous three-level distinction between explanations in cognitive science, it is often accepted that focus on modeling cognitive tasks should be on the computational level rather than the algorithmic level. When it comes to mathematical problem solving, this approach suggests that the complexity of the task of solving a problem can be characterized by the computational complexity of that problem. In this paper, I argue that human cognizers use heuristic and didactic tools and thus (...) engage in cognitive processes that make their problem solving algorithms computationally suboptimal, in contrast with the optimal algorithms studied in the computational approach. Therefore, in order to accurately model the human cognitive tasks involved in mathematical problem solving, we need to expand our methodology to also include aspects relevant to the algorithmic level. This allows us to study algorithms that are cognitively optimal for human problem solvers. Since problem solving methods are not universal, I propose that they should be studied in the framework of enculturation, which can explain the expected cultural variance in the humanly optimal algorithms. While mathematical problem solving is used as the case study, the considerations in this paper concern modeling of cognitive tasks in general. (shrink)

Marr’s seminal distinction between computational, algorithmic, and implementational levels of analysis has inspired research in cognitive science for more than 30 years. According to a widely-used paradigm, the modelling of cognitive processes should mainly operate on the computational level and be targeted at the idealised competence, rather than the actual performance of cognisers in a specific domain. In this paper, we explore how this paradigm can be adopted and revised to understand mathematical problem solving. The computational-level approach applies (...) methods from computational complexity theory and focuses on optimal strategies for completing cognitive tasks. However, human cognitive capacities in mathematical problem solving are essentially characterised by processes that are computationally sub-optimal, because they initially add to the computational complexity of the solutions. Yet, these solutions can be optimal for human cognisers given the acquisition and enactment of mathematical practices. Here we present diagrams and the spatial manipulation of symbols as two examples of problem solving strategies that can be computationally sub-optimal but humanly optimal. These aspects need to be taken into account when analysing competence in mathematical problem solving. Empirically informed considerations on enculturation can help identify, explore, and model the cognitive processes involved in problem solving tasks. The enculturation account of mathematical problem solving strongly suggests that computational-level analyses need to be complemented by considerations on the algorithmic and implementational levels. The emerging research strategy can help develop algorithms that model what we call enculturated cognitive optimality in an empirically plausible and ecologically valid way. (shrink)

We investigate flexibility and problem solving in skilled action. We conducted a field study of mountain bike riding that required a learner rider to cope with major changes in technique and equipment. Our results indicate that relatively inexperienced individuals can be capable of fairly complex 'on-the-fly' problem solving which allows them to cope with new conditions. This problem solving is hard to explain for classical theories of skill because the adjustments are too large (...) to be achieved by automatic mechanisms and too complex and rapid to be achieved by cognitive processes as they are usually understood. A recent theory, Mesh, can explain these results because it posits that skill-specific cognitive abilities develop during skill learning and that control typically involves an interplay between cognitive and automatic mechanisms. Here we develop Mesh further, providing a detailed explanation for these problem solving abilities. We argue that causal representation, metacognitive awareness and other forms of performance awareness combine in the formulation and control of action strategies. We also argue that the structure of control present in this case is inconsistent with Bratman's model of intentions, and that, in the face of high uncertainty and risk, intentions can be much more labile than Bratman recognises. In addition, we found limitations and flaws in problem solving which illuminate the representations involved. Finally, we highlight the crucial role of social and cultural learning in the development of complex skills. (shrink)

What are consequential world problems? As “grand societal challenges”, one might define them as problems that affect a large number of people, perhaps even the entire planet, including problems such as climate change, distributive justice, world peace, world nutrition, clean air and clean water, access to education, and many more. The “Sustainable Development Goals”, compiled by the United Nations, represent a collection of such global problems. From my point of view, these problems can be seen as complex. Such (...) class='Hi'>complex problems are characterized by the complexity, connectivity, dynamics, intransparency, and polytely of their underlying systems. These attributes require special competencies for dealing with the uncertainties of the given domains, e.g., critical thinking. My position is that it is not IQ, but complex problem-solving competencies for dealing with complex and dynamic situations, that is important for handling consequential global problems. These problems require system competencies, i.e., competencies that go beyond analytical intelligence, and comprise systems understanding as well as systems control. Complex problem-solving is more than analytic intelligence. (shrink)

The philosophy of mind is traditionally concerned with the study of mental processes, language, the representation of knowledge and the relation of the mind shares with the body; computational complexity theory is related to the classification of computationally solvable problems (be it via execution time, storage requirements, etc...). While there are well-established links between computer science in general & the philosophy of mind, many possible solutions to traditional problems in the philosophy of mind have not yet been analyzed from the (...) more specific lens of computational complexity theory. In his paper "Why Philosophers Should Care about Computational Complexity", Scott Aaronson argues that many conventional theories of epistemology & mind implicitly make the presupposition of omniscience (by supposing that knowing base facts means a knower necessarily understands derivative facts) - he proposes that computational complexity theory could explain why this is not the case. In this paper, I argue for a theory of mental representation & epistemology compatible with Aaronson's observations on complexity theory, overcoming that presupposition of omniscience. (shrink)

The deep crisis in modern fundamental science development is ever more evident and openly recognised now even by mainstream, official science professionals and leaders. By no coincidence, it occurs in parallel to the world civilisation crisis and related global change processes, where the true power of unreduced scientific knowledge is just badly missing as the indispensable and unique tool for the emerging greater problem solution and further progress at a superior level of complex world dynamics. Here we reveal (...) the mathematically exact reason for the crisis in conventional science, containing also the natural and unified problem solution in the form of well-specified extension of usual, artificially restricted paradigm. We show how that extended, now causally complete science content provides various "unsolvable" problem solutions and opens new development possibilities for both science and society, where the former plays the role of the main, direct driver for the latter. We outline the related qualitative changes in science organisation, practice and purposes, giving rise to the sustainability transition in the entire civilisation dynamics towards the well-specified superior level of its unreduced, now well understood and universally defined complexity. (shrink)

Analyzing causation in terms of Woodward's interventionist theory and describing the structure of the world in terms of causal powers are usually regarded as quite different projects in contemporary philosophy. Interventionists aim to give an account of how causal relations can be empirically discovered and described, without committing themselves to views about what causation really is. Causal powers theorists engage in precisely the latter project, aiming to describe the metaphysical structure of the world. In this paper, I argue that interventionism (...) can benefit from incorporating considerations about causal powers. I describe a previously undiscussed problem for Woodward's definition of an intervention variable that arises when interventionist causal models include disjunctive variables. This problem is solved not by excluding disjunctive (or logically compound) variables per se, but by excluding variables whose values represent disjunctions of too different causal powers. This suggests that interventionism and causal powers theories may be less distant from each other than is often assumed. (shrink)

Moral non-cognitivists hope to explain the nature of moral agreement and disagreement as agreement and disagreement in non-cognitive attitudes. In doing so, they take on the task of identifying the relevant attitudes, distinguishing the non-cognitive attitudes corresponding to judgements of moral wrongness, for example, from attitudes involved in aesthetic disapproval or the sports fan’s disapproval of her team’s performance. We begin this paper by showing that there is a simple recipe for generating apparent counterexamples to any informative specification of the (...) moral attitudes. This may appear to be a lethal objection to non-cognitivism, but a similar recipe challenges attempts by non-cognitivism’s competitors to specify the conditions underwriting the contrast between genuine and merely apparent moral disagreement. Because of its generality, this specification problem requires a systematic response, which, we argue, is most easily available for the non-cognitivist. Building on premisses congenial to the non-cognitivist tradition, we make the following claims: (1) In paradigmatic cases, wrongness-judgements constitute a certain complex but functionally unified state, and paradigmatic wrongness-judgements form a functional kind, preserved by homeostatic mechanisms. (2) Because of the practical function of such judgements, we should expect judges’ intuitive understanding of agreement and disagreement to be accommodating, treating states departing from the paradigm in various ways as wrongness-judgements. (3) This explains the intuitive judgements required by the counterexample-generating recipe, and more generally why various kinds of amoralists are seen as making genuine wrongness-judgements. (shrink)

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as (...) computational models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes. (shrink)

This article introduces and defends the “pathological complexity thesis” as a hypothesis about the evolutionary origins of minimal consciousness, or sentience, that connects the study of animal consciousness closely with work in behavioral ecology and evolutionary biology. I argue that consciousness is an adaptive solution to a design problem that led to the extinction of complex multicellular animal life following the Avalon explosion and that was subsequently solved during the Cambrian explosion. This is the economic trade-off problem (...) of having to deal with a complex body with high degrees of freedom, what I call “pathological complexity.” By modeling the explosion of this computational complexity using the resources of state-based behavioral and life history theory we will be able to provide an evolutionary bottom-up framework to make sense of subjective experience and its function in nature by paying close attention to the ecological lifestyles of different animals. (shrink)

Why should moral philosophers, moral psychologists, and machine ethicists care about computational complexity? Debates on whether artificial intelligence (AI) can or should be used to solve problems in ethical domains have mainly been driven by what AI can or cannot do in terms of human capacities. In this paper, we tackle the problem from the other end by exploring what kind of moral machines are possible based on what computational systems can or cannot do. To do so, we analyze (...) normative ethics through the lens of computational complexity. First, we introduce computational complexity for the uninitiated reader and discuss how the complexity of ethical problems can be framed within Marr’s three levels of analysis. We then study a range of ethical problems based on consequentialism, deontology, and virtue ethics, with the aim of elucidating the complexity associated with the problems themselves (e.g., due to combinatorics, uncertainty, strategic dynamics), the computational methods employed (e.g., probability, logic, learning), and the available resources (e.g., time, knowledge, learning). The results indicate that most problems the normative frameworks pose lead to tractability issues in every category analyzed. Our investigation also provides several insights about the computational nature of normative ethics, including the differences between rule- and outcome-based moral strategies, and the implementation-variance with regard to moral resources. We then discuss the consequences complexity results have for the prospect of moral machines in virtue of the trade-off between optimality and efficiency. Finally, we elucidate how computational complexity can be used to inform both philosophical and cognitive-psychological research on human morality by advancing the moral tractability thesis. (shrink)

The study determined the problem-solving performance and skills of prospective elementary teachers (PETs) in the Northern Philippines. Specifically, it defined the PETs’ level of problem-solving performance in number sense, measurement, geometry, algebra, and probability; significant predictors of their problem-solving performance in terms of sex, socio-economic status, parents’ educational attainment, high school graduated from and subject preference; and their problem-solving skills. The PETs’ problem-solving performance was determined by a problem set (...) consisting of word problems with number sense, measurement, geometry, algebra, and probability. A mixed-method research design was employed. Senior PETs purposively served as a sample where they mostly preferred to teach other subjects than mathematics. PETs who preferred math performed satisfactorily, while prospective teachers who opted for other subjects performed unsatisfactorily. The PETs’ unsatisfactory output indicates the need for remediation to advance the mathematical material skills and enrich the problem-solving abilities of these primary schools' potential teachers. Besides, results showed that subject preference strongly affected and predicted the problem-solving success of the PETs. PETs who preferred to teach mathematics performed significantly better than their counterparts; hence, mathematics as a field of specialization in the Bachelor of Elementary Education program may be considered by teacher education institutions. Further, most PETs displayed lack of problem-solving skills; thus, a Problem-Solving course is recommended for them. (shrink)

In this article I present an alternative philosophy of science based on ideas drawn from the study of complex adaptive systems. As a result of the spectacular expansion in scientific disciplines, the number of scientists and scientific institutions in the twentieth century, I believe science can be characterised as a complex system. I want to interpret the processes of science through which scientists themselves determine what counts as good science. This characterisation of science as a complex system (...) can give an answer to the question why the sciences are so successful in solving growing numbers of problems and correcting their own mistakes. I utilise components of complexity theory to explain and interpret science as a complex system. I first explain the concept of complexity in ordinary language. The explanation of science as a complex system starts with a definition of the basic rules that guide the behaviour of science as a complex system. Next, I show how various sciences result through the implementation of these rules in the study of a specific aspect of reality. The explanation of the growth of science through evolutionary adaptation and learning forms the core of the article. (shrink)

Behavior oftentimes allows for many possible interpretations in terms of mental states, such as goals, beliefs, desires, and intentions. Reasoning about the relation between behavior and mental states is therefore considered to be an effortful process. We argue that people use simple strategies to deal with high cognitive demands of mental state inference. To test this hypothesis, we developed a computational cognitive model, which was able to simulate previous empirical findings: In two-player games, people apply simple strategies at first. They (...) only start revising their strategies when these do not pay off. The model could simulate these findings by recursively attributing its own problem solving skills to the other player, thus increasing the complexity of its own inferences. The model was validated by means of a comparison with findings from a developmental study in which the children demonstrated similar strategic developments. (shrink)

Behavior oftentimes allows for many possible interpretations in terms of mental states, such as goals, beliefs, desires, and intentions. Reasoning about the relation between behavior and mental states is therefore considered to be an effortful process. We argue that people use simple strategies to deal with high cognitive demands of mental state inference. To test this hypothesis, we developed a computational cognitive model, which was able to simulate previous empirical findings: In two-player games, people apply simple strategies at first. They (...) only start revising their strategies when these do not pay off. The model could simulate these findings by recursively attributing its own problem solving skills to the other player, thus increasing the complexity of its own inferences. The model was validated by means of a comparison with findings from a developmental study in which the children demonstrated similar strategic developments. (shrink)

Behavior oftentimes allows for many possible interpretations in terms of mental states, such as goals, beliefs, desires, and intentions. Reasoning about the relation between behavior and mental states is therefore considered to be an effortful process. We argue that people use simple strategies to deal with high cognitive demands of mental state inference. To test this hypothesis, we developed a computational cognitive model, which was able to simulate previous empirical findings: In two-player games, people apply simple strategies at first. They (...) only start revising their strategies when these do not pay off. The model could simulate these findings by recursively attributing its own problem solving skills to the other player, thus increasing the complexity of its own inferences. The model was validated by means of a comparison with findings from a developmental study in which the children demonstrated similar strategic developments. (shrink)

Our intuition tells us that there is a general trend in the evolution of nature, a trend towards greater complexity. However, there are several definitions of complexity and hence it is difficult to argue for or against the validity of this intuition. Christoph Adami has recently introduced a novel measure called physical complexity that assigns low complexity to both ordered and random systems and high complexity to those in between. Physical complexity measures the amount of information that an organism stores (...) in its genome about the environment in which it evolves. The theory of physical complexity predicts that evolution increases the amount of ‘knowledge’ an organism accumulates about its niche. It might be fruitful to generalize Adami’s concept of complexity to the entire evolution (including the evolution of man). Physical complexity fits nicely into the philosophical framework of cognitive biology which considers biological evolution as a progressing process of accumulation of knowledge (as a gradual increase of epistemic complexity). According to this paradigm, evolution is a cognitive ‘ratchet’ that pushes the organisms unidirectionally towards higher complexity. Dynamic environment continually creates problems to be solved. To survive in the environment means to solve the problem, and the solution is an embodied knowledge. Cognitive biology (as well as the theory of physical complexity) uses the concepts of information and entropy and views the evolution from both the information-theoretical and thermodynamical perspective. Concerning humans as conscious beings, it seems necessary to postulate an emergence of a new kind of knowledge - a self-aware and self-referential knowledge. Appearence of selfreflection in evolution indicates that the human brain reached a new qualitative level in the epistemic complexity. (shrink)

Climatology is a paradigmatic complex systems science. Understanding the global climate involves tackling problems in physics, chemistry, economics, and many other disciplines. I argue that complex systems like the global climate are characterized by certain dynamical features that explain how those systems change over time. A complex system's dynamics are shaped by the interaction of many different components operating at many different temporal and spatial scales. Examining the multidisciplinary and holistic methods of climatology can help us better (...) understand the nature of complex systems in general. -/- Questions surrounding climate science can be divided into three rough categories: foundational, methodological, and evaluative questions. "How do we know that we can trust science?" is a paradigmatic foundational question (and a surprisingly difficult one to answer). Because the global climate is so complex, questions like "what makes a system complex?" also fall into this category. There are a number of existing definitions of `complexity,' and while all of them capture some aspects of what makes intuitively complex systems distinctive, none is entirely satisfactory. Most existing accounts of complexity have been developed to work with information-theoretic objects (signals, for instance) rather than the physical and social systems studied by scientists. -/- Dynamical complexity, a concept articulated in detail in the first third of the dissertation, is designed to bridge the gap between the mathematics of contemporary complexity theory (in particular the formalism of "effective complexity" developed by Gell-Mann and Lloyd [2003]) and a more general account of the structure of science generally. Dynamical complexity provides a physical interpretation of the formal tools of mathematical complexity theory, and thus can be used as a framework for thinking about general problems in the philosophy of science, including theories, explanation, and lawhood. -/- Methodological questions include questions about how climate science constructs its models, on what basis we trust those models, and how we might improve those models. In order to answer questions about climate modeling, it's important to understand what climate models look like and how they are constructed. Climate model families are significantly more diverse than are the model families of most other sciences (even sciences that study other complex systems). Existing climate models range from basic models that can be solved on paper to staggeringly complicated models that can only be analyzed using the most advanced supercomputers in the world. I introduce some of the central concepts in climatology by demonstrating how one of the most basic climate models might be constructed. I begin with the assumption that the Earth is a simple featureless blackbody which receives energy from the sun and releases it into space, and show how to model that assumption formally. I then gradually add other factors (e.g. albedo and the greenhouse effect) to the model, and show how each addition brings the model's prediction closer to agreement with observation. After constructing this basic model, I describe the so-called "complexity hierarchy" of the rest of climate models, and argue that the sense of "complexity" used in the climate modeling community is related to dynamical complexity. -/- With a clear understanding of the basics of climate modeling in hand, I then argue that foundational issues discussed early in the dissertation suggest that computation plays an irrevocably central role in climate modeling. "Science by simulation" is essential given the complexity of the global climate, but features of the climate system--the presence of non-linearities, feedback loops, and chaotic dynamics--put principled limits on the effectiveness of computational models. This tension is at the root of the staggering pluralism of the climate model hierarchy, and suggests that such pluralism is here to stay, rather than an artifact of our ignorance. Rather than attempting to converge on a single "best fit" climate model, we ought to embrace the diversity of climate models, and view each as a specialized tool designed to predict and explain a rather narrow range of phenomena. Understanding the climate system as a whole requires examining a number of different models, and correlating their outputs. This is the most significant methodological challenge of climatology. -/- Climatology's role contemporary political discourse raises an unusually high number of evaluative questions for a physical science. The two leading approaches to crafting policy surrounding climate change center on mitigation (i.e. stopping the changes from occurring) and adaptation (making post hoc changes to ameliorate the harm caused by those changes). Crafting an effective socio-political response to the threat of anthropogenic climate change, however, requires us to integrate multiple perspectives and values: the proper response will be just as diverse and pluralistic as the climate models themselves, and will incorporate aspects of both approaches. I conclude by offering some concrete recommendations about how to integrate this value pluralism into our socio-political decision making framework. (shrink)

Non-cognitivists are known to face a problem in extending their account of straightforward predicative moral judgments to logically complex moral judgments. This paper presents a related problem concerning how non-cognitivists might extend their accounts of moral judgments to other kinds of moral attitudes, such as moral hopes and moral intuitions. Non-cognitivists must solve three separate challenges: they must explain the natures of these other attitudes, they must explain why they count as moral attitudes, and they must explain (...) why the moral attitudes are systematically correlated with ordinary propositional attitudes. After presenting the problem, this paper examines several contemporary theories with some initial promise for solving it, and argues that they are insufficient. (shrink)

Math prospective teachers must be able to think creatively and solve problems. The study looked into preservice teachers’ creative thinking and problem-solving abilities in statistics. The investigation was guided by a correlational design in a public university in the Philippines. Stratified random sampling was used to select the 103 study participants from two teacher education programs. Through google forms, data were collected using Torrance et al. (2008)’s tests of creative thinking and researcher-made statistics problem test. The findings (...) revealed that preservice teachers have commendable creative thinking, particularly fluency, flexibility, and elaboration skills. Still, they lack problem-solving skills in statistics, specifically with central tendency, dispersion, and position measures. The correlational analysis revealed no link between creative thinking and problem-solving. Still, creative thinking and problem-solving courses are recommended to help preservice teachers develop their fundamental skills as mathematics educators. (shrink)

Operations research science is defined as the science that is concerned with applying scientific methods to complex problems in managing and directing large systems of people, including resources and tools in various fields, private and governmental work, peace and war, politics, administration, economics, planning and implementation in various domains. It uses scientific methods that take the language of mathematics as a basis for it and uses computer, without which it would not have been possible to achieve numerical solutions to (...) the raised problems, those that need correct solutions, when the solutions abound and the options are multiple, so we need a decision based on correct scientific foundations and takes into account all the circumstances and changes that you can encounter the decision-maker during the course of work, and nothing is left to chance or luck, but rather everything that enters into the account and plays its role in decision-making, and we get that when we use the concepts of neutrosophic science to reformulate what the science of operations research presented in terms of methods and methods to solve many practical problems, so we will present in this research a study aimed at shedding light on the most important methods used to solve nonlinear models, which is the Lagrangian multiplier method for nonlinear models constrained by equality and then reformulated using the concepts of neutrosophic science. (shrink)

Instead of postulated fixed structures and abstract principles of usual positivistic science, the unreduced diversity of living world reality is consistently derived as dynamically emerging results of unreduced interaction process development, starting from its simplest configuration of two coupled homogeneous protofields. The dynamically multivalued, or complex and intrinsically chaotic, nature of these real interaction results extends dramatically the artificially reduced, dynamically single-valued projection of standard theory and solves its stagnating old and accumulating new problems, “mysteries” and “paradoxes” within the (...) unified and causally complete picture of intrinsically evolving, dynamically complex reality. The permanently unfolding complexity progress thus revealed is fundamentally unlimited and does not need to stop at the directly observed diversity of usual matter complexity. The exciting, but rigorously substantiated and objectively inevitable prospects of further civilisation complexity development towards its superior levels of genuine sustainability and global Noosphere are outlined, with practically important conclusions for today’s critical problem solution. (shrink)

In the course of daily life we solve problems often enough that there is a special term to characterize the activity and the right to expect a scientific theory to explain its dynamics. The classical view in psychology is that to solve a problem a subject must frame it by creating an internal representation of the problem’s structure, usually called a problem space. This space is an internally generable representation that is mathematically identical to a graph structure (...) with nodes and links. The nodes can be annotated with useful information, and the whole representation can be distributed over internal and external structures such as symbolic notations on paper or diagrams. If the representation is distributed across internal and external structures the subject must be able to keep track of activity in the distributed structure. Problem solving proceeds as the subject works from an initial state in mentally supported space, actively constructing possible solution paths, evaluating them and heuristically choosing the best. Control of this exploratory process is not well understood, as it is not always systematic, but various heuristic search algorithms have been proposed and some experimental support has been provided for them. (shrink)

We present a novel approach to quantum gravity derived from maximizing the entropy of all possible geometric measurements. Multivector amplitudes emerge as the mathematical structure that solves this maximization problem in its full generality, superseding the complex amplitudes of standard quantum mechanics. The resulting multivector probability measure is invariant under a wide range of geometric transformations, and includes the Born rule as a special case. In this formalism, the gamma matrices become self-adjoint operators, enabling the construction of the (...) metric tensor as a quantum observable. The Schrödinger equation emerges as the active generator of arbitrary metric transformations, and the gauge symmetries SU(3)xSU(2)xU(1) of the Standard Model make their appearances without additional assumptions. Remarkably, the multivector amplitude formalism is found to be consistent only with 3+1-dimensional spacetime, encountering various obstructions in other dimensional configurations. The incorporation of the metric tensor as a quantum observable provides a natural pathway to integrate gravity with quantum mechanics. This entropy maximization approach to quantum gravity offers a parsimonious and unifying framework, bridging the gap between quantum theory and general relativity. (shrink)

This paper addresses the issue of how to best account for the diversity of our (synchronic) mental activities. The discussion starts with Mark Textor’s mental monism. According to mental monism, our mental life is constituted by just one simple mental act, in which different sub-acts can be conceptually distinguished. Textor grounds this view in the work of the early Brentano and contrasts it with the theory of the later Brentano, who introduces a mental substance into his philosophy. According to Textor, (...) Brentano needs a substance because he is unable to explain how mental monism can account for the separability of our mental activities, e.g. the fact that I can stop hearing F while still seeing blue. Textor argues, however, that mental monism can solve this problem. I address two issues regarding Textor’s view. First, I challenge his interpretation of Brentano by arguing that the early Brentano imports ontological complexity into our mental life; I defend Brentano’s view against possible criticisms, and I address some objections to mental monism. Second, I oppose Textor’s narrative about the mental substance. I argue that Brentano needs a substance not to explain separability, but rather to individuate our mental acts. I still argue, however, that Brentano’s earlier view (understood in my sense) is better than the substance account for dividing the mind. (shrink)

The Unexpected Hanging Problem is also known as the Surprise Examination Problem. We here solve it by isolating what is logical reasoning from the rest of the human psyche. In a not-so-orthodox analysis, following our tradition (The Liar, Dichotomy, The Sorites and Russell’s Paradox), we talk about the problem from a perspective that is more distant than all the known perspectives. From an observational point that is in much farther than all the observational points used until now, (...) the reader can finally see why the problem has been perpetuated as a problem and can also see that the problem was never an actual problem: Once more, we have an allurement. The allurement this time makes us start paying attention to all the complexity of the human psyche when studying problems that involve human feelings. The main finding could be told to be that we have to understand and study more the human psyche, in all its intricacies, also when dealing with problems that seem to belong with exclusivity to Mathematics or Logic. (shrink)

The ability to solve problems is a prerequisite in preparing mathematics preservice teachers. This study assessed preservice teachers’ problem-solving difficulties and performance, particularly in worded problems on number sense, measurement, geometry, algebra, and probability. Also, academic profile differences in the preservice teacher’s problem-solving performance and common errors were determined. A descriptive-comparative research design was employed with 158 random respondents. Data were gathered face-to-face during the first semester of the school year 2022-2023, and data were analyzed with (...) the aid of jamovi software, ensuring ethical measures. Overall findings revealed that the preservice teachers experienced average difficulty in solving problems. The low performance of the preservice teachers on the given problems was also demonstrated. Further analysis revealed a significant difference between the preservice teachers’ problem-solving performance based on their subject preference and program. Moreover, the error analysis revealed that the preservice teachers incurred comprehension errors in misrepresentation, misinterpretation, and miscalculation. These results will serve as a measure for policymakers and curriculum developers of the teacher education institution concerned to make relevant enhancements to the math courses offered in the elementary and secondary education programs. (shrink)

This study focused on the significant relationship between Creative Thinking Skills and Problem-Solving Skills in Mathematics among Grade 6 pupils. The study's respondents were thirty (30) Grade 6 pupils from one of the elementary schools in the District of Sta. Ana, Pampanga. The respondents were selected using simple random sampling techniques. The study used a survey questionnaire comprising the Creative Thinking Skills Test (Pentang et al., 2022) and a researcher-made word problem-solving written test and rubrics. The (...) researchers found a high level of Creative Thinking Skills among the Grade 6 pupils, while the respondents' problem-solving skills were categorized as competent. The study revealed that the Creative Thinking Skills and Problem-Solving Skills in Mathematics of the Grade 6 pupils were very lowly correlated. Still, creative thinking and problem-solving in the applied subject are recommended to help students acquire the 21st-century skills that empower them to develop holistically and career ready. (shrink)

Abstract. Competition between developed and developing countries in developing the defense industry in the era of globalization has crossed the boundaries of a country's alliances. However, in the transfer of technology (ToT) process, it remains the object of domination by large countries, and developing countries remain confined in a rigid bureaucracy. Researchers offer a problem-solving approach to developing the defense industry experienced by developing countries. The researcher's first step describes the bureaucracy of developing countries, and then the researcher (...) projects the development of a strategy as a solution. The researcher realizes that the trial and error approach offered by Karl R. Popper demands further testing, so the researcher also explains the weaknesses of the solutions offered. The researcher concludes that the Problem-Solving approach can solve problems and anticipate problems. Problem-Solving is no longer seen as containing a simple method but an epistemology; Solutions appear before the problem itself appears. The researcher corrected the problem- solving position, as explained by Ian Angus, who moved from one line to a new line continuously. Researchers see not moving lines and continuing but reality entering a broader flow. (shrink)

Humans have distinctive powers of reflection: no other animal seems to have anything like our capacity for self-examination. Many philosophers hold that this capacity has a uniquely important guiding role in our cognition; others, notably Hilary Kornblith, draw attention to its weaknesses. Kornblith chiefly aims to dispel the sense that there is anything ‘magical’ about second-order mental states, situating them in the same causal net as ordinary first-order mental states. But elsewhere he goes further, suggesting that there is something deeply (...) misleading about reflection’s first-person view of cognition. This chapter takes a closer look at the conditions under which reflection is misleading. Even if humans are the only reflective animals, we are no longer the only creatures that can be questioned about their claims. Chatbots can also be asked to explain themselves, and by studying the conditions under which they produce clarification as opposed to confabulation, we can develop a non-skeptical account of the epistemic value of reflection. I argue that this capacity naturally supports the distribution of complex problem solving among multiple agents. (shrink)

Elementary preservice teachers (EPTs) substantially impact the quality of mathematics education, and their subject preference and problem-solving performance are essential indicators of their readiness to teach. The study described EPTs’ subject preference and problem-solving performance. Through a sequential explanatory research design, the quantitative inquiry involved 125 random samples, while the qualitative inquiry was participated by 30 non-random samples. Data were obtained by using an online survey and conferencing. Quantitative data were analyzed through descriptive statistics and analysis (...) of variance, whereas qualitative data were themed accordingly. The EPTs displayed unsatisfactory problem-solving performance and preferred to handle subjects other than math. Besides, the analysis found no significant performance differences with the EPTs’ subject preferences. Further, the EPTs who preferred to teach mathematics expressed their confidence in mathematics. Meanwhile, the EPTs who preferred other subjects displayed math avoidance. The study revealed an alarming result indicating that the EPTs are unprepared for teaching. As agents in cultivating the nation’s mathematics education status, these EPTs must be equipped with fundamental content knowledge. It is suggested that educational decision-makers take measures to address the issues identified concerning EPTs’ readiness to teach mathematics successfully. (shrink)

Unlike human soldiers, autonomous weapons systems are unaffected by psychological factors that would cause them to act outside the chain of command. This is a compelling moral justification for their development and eventual deployment in war. To achieve this level of sophistication, the software that runs AWS will have to first solve two problems: the frame problem and the representation problem. Solutions to these problems will inevitably involve complex software. Complex software will create security risks and (...) will make AWS critically vulnerable to hacking. I claim that the political and tactical consequences of hacked AWS far outweigh the purported advantages of AWS not being affected by psychological factors and always following orders. Therefore, one of the moral justifications for the deployment of AWS is undermined. (shrink)

In this article, I shall argue that AI’s likely developments and possible challenges are best understood if we interpret AI not as a marriage between some biological-like intelligence and engineered artefacts, but as a divorce between agency and intelligence, that is, the ability to solve problems successfully and the necessity of being intelligent in doing so. I shall then look at five developments: (1) the growing shift from logic to statistics, (2) the progressive adaptation of the environment to AI rather (...) than of AI to the environment, (3) the increasing translation of difficult problems into complex problems, (4) the tension between regulative and constitutive rules underpinning areas of AI application, and (5) the push for synthetic data. (shrink)

This paper provides a principled and elegant solution to the Gettier problem. The key move is to draw a general metaphysical distinction and conscript it for epistemological purposes. Section 1 introduces the Gettier problem. Sections 2–5 discuss instructively wrong or incomplete previous proposals. Section 6 presents my solution and explains its virtues. Section 7 answers the most common objection.

Ernst Mach's atomistic theory of sensation faces problems in doing justice to our ability to perceive and remember complex phenomena such as melodies and shapes. Christian von Ehrenfels attempted to solve these problems with his theory of "Gestalt qualities", which he sees as entities depending one-sidedly on the corresponding simple objects of sensation. We explore the theory of dependence relations advanced by Ehrenfels and show how it relates to the views on the objects of perception advanced by Husserl and (...) by the Gestalt psychologists. (shrink)

An account of scientific explanation is presented according to which (1) scientific explanation consists in solving “insight” problems (Metcalfe and Wiebe 1984) and (2) understanding is the result of solving such problems. The theory is pragmatic; it draws upon van Fraassen’s (1977, 1980) insights, avoids the objections to pragmatic accounts offered by Kitcher and Salmon (1987), and relates scientific explanation directly to understanding. The theory also accommodates cases of explanatory asymmetry and intuitively legitimate rejections of explanation requests.

The main purpose of the study is to understand the mathematical problem-solving strategies among student teachers. This study used both quantitative and qualitative type of research. Aside from the semi-structured interviews, data were gathered through participant's actual mathematical problem-solving outputs and the videotaped interviews. Findings revealed that the problem-solving strategies among student teachers in the Problem-Solving subject are cognitive, metacognitive and other strategies. The cognitive strategies used by the student teachers are rehearsal, (...) elaboration, and organization. The metacognitive strategies are critical thinking and self-regulation. Other strategies are overlapping the cognitive and metacognitive strategies. These are prediction/orientation, planning, monitoring, and evaluating. The findings also suggest a significant influence of the strategies to the academic performance of the student teachers. (shrink)

A rigorous approach to the study of the mind–body problem is suggested. Since humans are able to talk about consciousness (produce phenomenal judgments), it is argued that the study of neural mechanisms of phenomenal judgments can solve the hard problem of consciousness. Particular methods are suggested for: (1) verification and falsification of materialism; (2) verification and falsification of interactionism; (3) falsification of epiphenomenalism and parallelism (verification is problematic); (4) verification of particular materialistic theories of consciousness; (5) a non-Turing (...) test for machine consciousness. A complex research program is constructed that includes studies of intelligent machines, numerical models of human and artificial creatures, language, neural correlates of con- sciousness, and quantum mechanisms in brain. (shrink)

The use of protocol analysis in the traning of cognitive skills.

In this paper, I draw attention to an obstacle to determining to what extent the portrait of normal science as a problem-solving activity applies outside the natural sciences. I give two examples from social anthropology, one from the heyday of British structural-functionalism and one from recent British anthropology, “responding” to Marilyn Strathern’s problem of the feminist fieldworker. (NOTE: there is a duplicate of this but neither may be showing on my profile. A proverb: the guest hates the (...) other guest; the host hates them both.). (shrink)

In this paper, I draw attention to an obstacle to determining to what extent the portrait of normal science as a problem-solving activity applies outside the natural sciences. I give two examples from social anthropology, one from the heyday of British structural-functionalism and one from recent British anthropology, “responding” to Marilyn Strathern's problem of the feminist fieldworker. (NOTE: There is a duplicate of this paper on PhilPapers!).

The urgent need of developing novel teaching methods in education to improve the critical thinking skills has been widely discussed by educational experts. The present study aims to investigate the effectiveness of Fermi problem solving with flipped learning techniques in teaching physics on the improvement of critical thinking skills among Emirati tenth graders. The sample of the study consists of 40 male and female secondary students from two secondary schools belonging to Abu Dhabi Department of Education and Knowledge (...) in United Arab Emirates divided into two groups; the control group consists of 20 students (10 male and 10 female) taught the physics unit by traditional methods, the experimental group consists of 20 students (10 males and 10 females) taught the physics unit by Fermi problem solving with flipped learning techniques. The quasi-experimental design was used, where the modified critical thinking skills test was prepared and administered on the two groups as a pre-test before the students start the treatment and as a post-test once they are finished. The MANCOVA and Two-Way ANCOVA tests were employed to analyze the data. The findings showed that there were statistically significant differences at (α = 0.05) in student’s critical thinking skills test (in favor of experimental group), indicating that the performance of students in treatment group was better than the control group in the post-test. This means that the Fermi problem solving with flipped learning techniques has significant effectiveness on improvement of critical thinking skills among the United Arab Emirates secondary students. Also there were no statistically significant differences between male and female students. (shrink)

In the present research, the authors hypothesized that additive counterfactual thinking mind-sets, activated by adding new antecedent elements to reconstruct reality, promote an expansive processing style that broadens conceptual attention and facilitates performance on creative generation tasks, whereas subtractive counterfactual thinking mind-sets, activated by removing antecedent elements to reconstruct reality, promote a relational processing style that enhances tendencies to consider relationships and associations and facilitates performance on analytical problem-solving tasks. A reanalysis of a published data set suggested that (...) the counterfactual mind-set primes previously used in the literature tend to evoke subtractive counterfactuals. Studies 1 and 2 then demonstrated that subtractive counterfactual mind-sets enhanced performance on analytical problem-solving tasks relative to additive counterfactual mind-sets, whereas Studies 3 and 4 found that additive counterfactual mind-sets enhanced performance on creative generation tasks relative to subtractive counterfactual mind-sets. (shrink)

The paper identifies defining characteristics of the principal models of problem-solving behavior which are useful in developing a general theory of problem-solving. An attempt is made both to make explicit those disagreements between theorists of different persuasions which have served as obstacles to an integrated approach, and to show that these disagreements have arisen from a number of conceptual confusions: The conflict between information processors and behavioral analysts has resulted from a common failure to understand theoretical (...) sufficiency, and hence these theorists have been at a loss to understand one another. Two directions of research in problem-solving, mechanical algorithmic problem-solving and the psychology of invention, have been thought to be divergent, but in fact complement one another once it is clear that problem-solving involves neither discovery nor invention, but rather is a matter of perceptual encoding and processing. Successful problem-solving behavior can be described as adaptive, learning behavior in which organization skills are effectively associated with situationally determined perceptual encoding processes of the individual mechanical or biological problem-solver. (shrink)